LMFDB - Embedded newform 350.4.j.d.149.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [350,4,Mod(149,350)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("350.149"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(350, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 2])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	350.j (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,8,0,8,0,0,-52,0,-70] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$20.6506685020$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			149.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	350.149
Dual form			350.4.j.d.249.2

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.73205 + 1.00000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(2.00000 + 3.46410i) q^{4} +2.00000 q^{6} +(-15.5885 - 10.0000i) q^{7} +8.00000i q^{8} +(-13.0000 + 22.5167i) q^{9} +(-17.5000 - 30.3109i) q^{11} +(3.46410 + 2.00000i) q^{12} -66.0000i q^{13} +(-17.0000 - 32.9090i) q^{14} +(-8.00000 + 13.8564i) q^{16} +(51.0955 - 29.5000i) q^{17} +(-45.0333 + 26.0000i) q^{18} +(68.5000 - 118.645i) q^{19} +(-18.5000 - 0.866025i) q^{21} -70.0000i q^{22} +(-6.06218 - 3.50000i) q^{23} +(4.00000 + 6.92820i) q^{24} +(66.0000 - 114.315i) q^{26} +53.0000i q^{27} +(3.46410 - 74.0000i) q^{28} -106.000 q^{29} +(-37.5000 - 64.9519i) q^{31} +(-27.7128 + 16.0000i) q^{32} +(-30.3109 - 17.5000i) q^{33} +118.000 q^{34} -104.000 q^{36} +(-9.52628 - 5.50000i) q^{37} +(237.291 - 137.000i) q^{38} +(-33.0000 - 57.1577i) q^{39} -498.000 q^{41} +(-31.1769 - 20.0000i) q^{42} -260.000i q^{43} +(70.0000 - 121.244i) q^{44} +(-7.00000 - 12.1244i) q^{46} +(148.090 + 85.5000i) q^{47} +16.0000i q^{48} +(143.000 + 311.769i) q^{49} +(29.5000 - 51.0955i) q^{51} +(228.631 - 132.000i) q^{52} +(361.133 - 208.500i) q^{53} +(-53.0000 + 91.7987i) q^{54} +(80.0000 - 124.708i) q^{56} -137.000i q^{57} +(-183.597 - 106.000i) q^{58} +(-8.50000 - 14.7224i) q^{59} +(-25.5000 + 44.1673i) q^{61} -150.000i q^{62} +(427.817 - 221.000i) q^{63} -64.0000 q^{64} +(-35.0000 - 60.6218i) q^{66} +(380.185 - 219.500i) q^{67} +(204.382 + 118.000i) q^{68} -7.00000 q^{69} -784.000 q^{71} +(-180.133 - 104.000i) q^{72} +(-255.477 + 147.500i) q^{73} +(-11.0000 - 19.0526i) q^{74} +548.000 q^{76} +(-30.3109 + 647.500i) q^{77} -132.000i q^{78} +(-247.500 + 428.683i) q^{79} +(-324.500 - 562.050i) q^{81} +(-862.561 - 498.000i) q^{82} -932.000i q^{83} +(-34.0000 - 65.8179i) q^{84} +(260.000 - 450.333i) q^{86} +(-91.7987 + 53.0000i) q^{87} +(242.487 - 140.000i) q^{88} +(-436.500 + 756.040i) q^{89} +(-660.000 + 1028.84i) q^{91} -28.0000i q^{92} +(-64.9519 - 37.5000i) q^{93} +(171.000 + 296.181i) q^{94} +(-16.0000 + 27.7128i) q^{96} -290.000i q^{97} +(-64.0859 + 683.000i) q^{98} +910.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{4} + 8 q^{6} - 52 q^{9} - 70 q^{11} - 68 q^{14} - 32 q^{16} + 274 q^{19} - 74 q^{21} + 16 q^{24} + 264 q^{26} - 424 q^{29} - 150 q^{31} + 472 q^{34} - 416 q^{36} - 132 q^{39} - 1992 q^{41} + 280 q^{44}+ \cdots + 3640 q^{99}+O(q^{100}) $ 4 * q + 8 * q^4 + 8 * q^6 - 52 * q^9 - 70 * q^11 - 68 * q^14 - 32 * q^16 + 274 * q^19 - 74 * q^21 + 16 * q^24 + 264 * q^26 - 424 * q^29 - 150 * q^31 + 472 * q^34 - 416 * q^36 - 132 * q^39 - 1992 * q^41 + 280 * q^44 - 28 * q^46 + 572 * q^49 + 118 * q^51 - 212 * q^54 + 320 * q^56 - 34 * q^59 - 102 * q^61 - 256 * q^64 - 140 * q^66 - 28 * q^69 - 3136 * q^71 - 44 * q^74 + 2192 * q^76 - 990 * q^79 - 1298 * q^81 - 136 * q^84 + 1040 * q^86 - 1746 * q^89 - 2640 * q^91 + 684 * q^94 - 64 * q^96 + 3640 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.73205	+	1.00000i	0.612372	+	0.353553i
$2$	1.73205	+	1.00000i	0.612372	+	0.353553i
$3$	0.866025	−	0.500000i	0.166667	−	0.0962250i	−0.414346	−	0.910119i	$-0.635990\pi$
$3$	0.866025	−	0.500000i	0.166667	−	0.0962250i	0.581013	+	0.813894i	$0.302656\pi$
$4$	2.00000	+	3.46410i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	2.00000			0.136083
$7$	−15.5885	−	10.0000i	−0.841698	−	0.539949i
$7$	−15.5885	−	10.0000i	−0.841698	−	0.539949i
$8$			8.00000i			0.353553i
$9$	−13.0000	+	22.5167i	−0.481481	+	0.833950i
$10$		0			0
$11$	−17.5000	−	30.3109i	−0.479677	−	0.830825i	0.520051	−	0.854135i	$-0.325913\pi$
$11$	−17.5000	−	30.3109i	−0.479677	−	0.830825i	−0.999728	+	0.0233099i	$0.992580\pi$
$12$	3.46410	+	2.00000i	0.0833333	+	0.0481125i
$13$		−	66.0000i		−	1.40809i	−0.710158	−	0.704043i	$-0.751376\pi$
$13$		−	66.0000i		−	1.40809i	0.710158	−	0.704043i	$-0.248624\pi$
$14$	−17.0000	−	32.9090i	−0.324532	−	0.628235i
$15$		0			0
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	51.0955	−	29.5000i	0.728969	−	0.420871i	−0.0890757	−	0.996025i	$-0.528391\pi$
$17$	51.0955	−	29.5000i	0.728969	−	0.420871i	0.818045	+	0.575154i	$0.195058\pi$
$18$	−45.0333	+	26.0000i	−0.589692	+	0.340459i
$19$	68.5000	−	118.645i	0.827104	−	1.43259i	−0.0731965	−	0.997318i	$-0.523320\pi$
$19$	68.5000	−	118.645i	0.827104	−	1.43259i	0.900301	−	0.435269i	$-0.143347\pi$
$20$		0			0
$21$	−18.5000	−	0.866025i	−0.192240	−	0.00899915i
$22$		−	70.0000i		−	0.678366i
$23$	−6.06218	−	3.50000i	−0.0549588	−	0.0317305i	0.472269	−	0.881455i	$-0.343435\pi$
$23$	−6.06218	−	3.50000i	−0.0549588	−	0.0317305i	−0.527228	+	0.849724i	$0.676768\pi$
$24$	4.00000	+	6.92820i	0.0340207	+	0.0589256i
$25$		0			0
$26$	66.0000	−	114.315i	0.497833	−	0.862273i
$27$			53.0000i			0.377772i
$28$	3.46410	−	74.0000i	0.0233805	−	0.499453i
$29$	−106.000			−0.678748			−0.339374	−	0.940651i	$-0.610215\pi$
$29$	−106.000			−0.678748			−0.339374	+	0.940651i	$0.610215\pi$
$30$		0			0
$31$	−37.5000	−	64.9519i	−0.217264	−	0.376313i	0.736706	−	0.676213i	$-0.236380\pi$
$31$	−37.5000	−	64.9519i	−0.217264	−	0.376313i	−0.953971	+	0.299900i	$0.903047\pi$
$32$	−27.7128	+	16.0000i	−0.153093	+	0.0883883i
$33$	−30.3109	−	17.5000i	−0.159892	−	0.0923139i
$34$	118.000			0.595201
$35$		0			0
$36$	−104.000			−0.481481
$37$	−9.52628	−	5.50000i	−0.0423273	−	0.0244377i	0.478687	−	0.877986i	$-0.341113\pi$
$37$	−9.52628	−	5.50000i	−0.0423273	−	0.0244377i	−0.521014	+	0.853548i	$0.674446\pi$
$38$	237.291	−	137.000i	1.01299	−	0.584851i
$39$	−33.0000	−	57.1577i	−0.135493	−	0.234681i
$40$		0			0
$41$	−498.000			−1.89694			−0.948470	−	0.316867i	$-0.897369\pi$
$41$	−498.000			−1.89694			−0.948470	+	0.316867i	$0.897369\pi$
$42$	−31.1769	−	20.0000i	−0.114541	−	0.0734778i
$43$		−	260.000i		−	0.922084i	−0.887378	−	0.461042i	$-0.847476\pi$
$43$		−	260.000i		−	0.922084i	0.887378	−	0.461042i	$-0.152524\pi$
$44$	70.0000	−	121.244i	0.239839	−	0.415413i
$45$		0			0
$46$	−7.00000	−	12.1244i	−0.0224368	−	0.0388617i
$47$	148.090	+	85.5000i	0.459600	+	0.265350i	0.711876	−	0.702305i	$-0.247846\pi$
$47$	148.090	+	85.5000i	0.459600	+	0.265350i	−0.252276	+	0.967655i	$0.581179\pi$
$48$			16.0000i			0.0481125i
$49$	143.000	+	311.769i	0.416910	+	0.908948i
$50$		0			0
$51$	29.5000	−	51.0955i	0.0809966	−	0.140290i
$52$	228.631	−	132.000i	0.609719	−	0.352021i
$53$	361.133	−	208.500i	0.935951	−	0.540371i	0.0472619	−	0.998883i	$-0.484950\pi$
$53$	361.133	−	208.500i	0.935951	−	0.540371i	0.888689	+	0.458511i	$0.151617\pi$
$54$	−53.0000	+	91.7987i	−0.133563	+	0.231337i
$55$		0			0
$56$	80.0000	−	124.708i	0.190901	−	0.297585i
$57$		−	137.000i		−	0.318353i
$58$	−183.597	−	106.000i	−0.415647	−	0.239974i
$59$	−8.50000	−	14.7224i	−0.0187560	−	0.0324864i	0.856495	−	0.516155i	$-0.172637\pi$
$59$	−8.50000	−	14.7224i	−0.0187560	−	0.0324864i	−0.875251	+	0.483669i	$0.839304\pi$
$60$		0			0
$61$	−25.5000	+	44.1673i	−0.0535236	+	0.0927056i	−0.891546	−	0.452930i	$-0.850379\pi$
$61$	−25.5000	+	44.1673i	−0.0535236	+	0.0927056i	0.838022	+	0.545636i	$0.183712\pi$
$62$		−	150.000i		−	0.307258i
$63$	427.817	−	221.000i	0.855553	−	0.441958i
$64$	−64.0000			−0.125000
$65$		0			0
$66$	−35.0000	−	60.6218i	−0.0652758	−	0.113061i
$67$	380.185	−	219.500i	0.693239	−	0.400242i	−0.111585	−	0.993755i	$-0.535593\pi$
$67$	380.185	−	219.500i	0.693239	−	0.400242i	0.804824	+	0.593513i	$0.202260\pi$
$68$	204.382	+	118.000i	0.364485	+	0.210435i
$69$	−7.00000			−0.0122131
$70$		0			0
$71$	−784.000			−1.31047			−0.655237	−	0.755423i	$-0.727431\pi$
$71$	−784.000			−1.31047			−0.655237	+	0.755423i	$0.727431\pi$
$72$	−180.133	−	104.000i	−0.294846	−	0.170229i
$73$	−255.477	+	147.500i	−0.409608	+	0.236487i	−0.690621	−	0.723217i	$-0.742663\pi$
$73$	−255.477	+	147.500i	−0.409608	+	0.236487i	0.281013	+	0.959704i	$0.409329\pi$
$74$	−11.0000	−	19.0526i	−0.0172801	−	0.0299299i
$75$		0			0
$76$	548.000			0.827104
$77$	−30.3109	+	647.500i	−0.0448603	+	0.958305i
$78$		−	132.000i		−	0.191616i
$79$	−247.500	+	428.683i	−0.352480	+	0.610513i	−0.986683	−	0.162653i	$-0.947995\pi$
$79$	−247.500	+	428.683i	−0.352480	+	0.610513i	0.634203	+	0.773166i	$0.281328\pi$
$80$		0			0
$81$	−324.500	−	562.050i	−0.445130	−	0.770988i
$82$	−862.561	−	498.000i	−1.16163	−	0.670670i
$83$		−	932.000i		−	1.23253i	−0.787537	−	0.616267i	$-0.788644\pi$
$83$		−	932.000i		−	1.23253i	0.787537	−	0.616267i	$-0.211356\pi$
$84$	−34.0000	−	65.8179i	−0.0441631	−	0.0854920i
$85$		0			0
$86$	260.000	−	450.333i	0.326006	−	0.564659i
$87$	−91.7987	+	53.0000i	−0.113125	+	0.0653126i
$88$	242.487	−	140.000i	0.293741	−	0.169591i
$89$	−436.500	+	756.040i	−0.519875	+	0.900451i	0.479858	+	0.877346i	$0.340688\pi$
$89$	−436.500	+	756.040i	−0.519875	+	0.900451i	−0.999733	+	0.0231042i	$0.992645\pi$
$90$		0			0
$91$	−660.000	+	1028.84i	−0.760294	+	1.18518i
$92$		−	28.0000i		−	0.0317305i
$93$	−64.9519	−	37.5000i	−0.0724215	−	0.0418126i
$94$	171.000	+	296.181i	0.187631	+	0.324986i
$95$		0			0
$96$	−16.0000	+	27.7128i	−0.0170103	+	0.0294628i
$97$		−	290.000i		−	0.303557i	−0.988415	−	0.151779i	$-0.951500\pi$
$97$		−	290.000i		−	0.303557i	0.988415	−	0.151779i	$-0.0485001\pi$
$98$	−64.0859	+	683.000i	−0.0660577	+	0.704014i
$99$	910.000			0.923823
$100$		0			0
$101$	542.500	+	939.638i	0.534463	+	0.925717i	0.999189	+	0.0402627i	$0.0128195\pi$
$101$	542.500	+	939.638i	0.534463	+	0.925717i	−0.464726	+	0.885454i	$0.653847\pi$
$102$	102.191	−	59.0000i	0.0992002	−	0.0572732i
$103$	1344.94	+	776.500i	1.28661	+	0.742823i	0.978048	−	0.208381i	$-0.0668195\pi$
$103$	1344.94	+	776.500i	1.28661	+	0.742823i	0.308560	+	0.951205i	$0.400153\pi$
$104$	528.000			0.497833
$105$		0			0
$106$	834.000			0.764200
$107$	−111.717	−	64.5000i	−0.100936	−	0.0582752i	0.448682	−	0.893691i	$-0.351893\pi$
$107$	−111.717	−	64.5000i	−0.100936	−	0.0582752i	−0.549618	+	0.835416i	$0.685227\pi$
$108$	−183.597	+	106.000i	−0.163580	+	0.0944431i
$109$	−482.500	−	835.715i	−0.423992	−	0.734376i	0.572334	−	0.820021i	$-0.306038\pi$
$109$	−482.500	−	835.715i	−0.423992	−	0.734376i	−0.996326	+	0.0856452i	$0.972705\pi$
$110$		0			0
$111$	−11.0000			−0.00940607
$112$	263.272	−	136.000i	0.222115	−	0.114739i
$113$			50.0000i			0.0416248i	0.999783	+	0.0208124i	$0.00662527\pi$
$113$			50.0000i			0.0416248i	−0.999783	+	0.0208124i	$0.993375\pi$
$114$	137.000	−	237.291i	0.112555	−	0.194950i
$115$		0			0
$116$	−212.000	−	367.195i	−0.169687	−	0.293907i
$117$	1486.10	+	858.000i	1.17427	+	0.677967i
$118$		−	34.0000i		−	0.0265250i
$119$	−1091.50	−	51.0955i	−0.840821	−	0.0393606i
$120$		0			0
$121$	53.0000	−	91.7987i	0.0398197	−	0.0689697i
$122$	−88.3346	+	51.0000i	−0.0655528	+	0.0378469i
$123$	−431.281	+	249.000i	−0.316157	+	0.182533i
$124$	150.000	−	259.808i	0.108632	−	0.188157i
$125$		0			0
$126$	962.000	+	45.0333i	0.680173	+	0.0318404i
$127$			936.000i			0.653989i	0.945026	+	0.326994i	$0.106036\pi$
$127$			936.000i			0.653989i	−0.945026	+	0.326994i	$0.893964\pi$
$128$	−110.851	−	64.0000i	−0.0765466	−	0.0441942i
$129$	−130.000	−	225.167i	−0.0887276	−	0.153681i
$130$		0			0
$131$	377.500	−	653.849i	0.251773	−	0.436084i	−0.712241	−	0.701935i	$-0.752320\pi$
$131$	377.500	−	653.849i	0.251773	−	0.436084i	0.964014	+	0.265851i	$0.0856529\pi$
$132$		−	140.000i		−	0.0923139i
$133$	−2254.26	+	1164.50i	−1.46970	+	0.759210i
$134$	878.000			0.566027
$135$		0			0
$136$	236.000	+	408.764i	0.148800	+	0.257730i
$137$	−2041.22	+	1178.50i	−1.27294	+	0.734935i	−0.975541	−	0.219817i	$-0.929454\pi$
$137$	−2041.22	+	1178.50i	−1.27294	+	0.734935i	−0.297403	+	0.954752i	$0.596121\pi$
$138$	−12.1244	−	7.00000i	−0.00747894	−	0.00431797i
$139$	−28.0000			−0.0170858			−0.00854291	−	0.999964i	$-0.502719\pi$
$139$	−28.0000			−0.0170858			−0.00854291	+	0.999964i	$0.502719\pi$
$140$		0			0
$141$	171.000			0.102133
$142$	−1357.93	−	784.000i	−0.802498	−	0.463323i
$143$	−2000.52	+	1155.00i	−1.16987	+	0.675426i
$144$	−208.000	−	360.267i	−0.120370	−	0.208488i
$145$		0			0
$146$	−590.000			−0.334443
$147$	279.726	+	198.500i	0.156948	+	0.111374i
$148$		−	44.0000i		−	0.0244377i
$149$	1147.50	−	1987.53i	0.630919	−	1.09278i	−0.356446	−	0.934316i	$-0.616012\pi$
$149$	1147.50	−	1987.53i	0.630919	−	1.09278i	0.987364	−	0.158467i	$-0.0506551\pi$
$150$		0			0
$151$	554.500	+	960.422i	0.298838	+	0.517603i	0.975870	−	0.218350i	$-0.0700676\pi$
$151$	554.500	+	960.422i	0.298838	+	0.517603i	−0.677032	+	0.735953i	$0.736734\pi$
$152$	949.164	+	548.000i	0.506496	+	0.292425i
$153$			1534.00i			0.810566i
$154$	−700.000	+	1091.19i	−0.366283	+	0.570979i
$155$		0			0
$156$	132.000	−	228.631i	0.0677465	−	0.117340i
$157$	1350.13	−	779.500i	0.686321	−	0.396248i	−0.115911	−	0.993260i	$-0.536979\pi$
$157$	1350.13	−	779.500i	0.686321	−	0.396248i	0.802232	+	0.597012i	$0.203646\pi$
$158$	−857.365	+	495.000i	−0.431698	+	0.249241i
$159$	208.500	−	361.133i	0.103995	−	0.180124i
$160$		0			0
$161$	59.5000	+	115.181i	0.0291258	+	0.0563824i
$162$		−	1298.00i		−	0.629509i
$163$	−1949.42	−	1125.50i	−0.936752	−	0.540834i	−0.0478115	−	0.998856i	$-0.515225\pi$
$163$	−1949.42	−	1125.50i	−0.936752	−	0.540834i	−0.888941	+	0.458022i	$0.848558\pi$
$164$	−996.000	−	1725.12i	−0.474235	−	0.821399i
$165$		0			0
$166$	932.000	−	1614.27i	0.435766	−	0.754770i
$167$			2788.00i			1.29187i	0.763393	+	0.645934i	$0.223532\pi$
$167$			2788.00i			1.29187i	−0.763393	+	0.645934i	$0.776468\pi$
$168$	6.92820	−	148.000i	0.00318168	−	0.0679670i
$169$	−2159.00			−0.982704
$170$		0			0
$171$	1781.00	+	3084.78i	0.796471	+	1.37953i
$172$	900.666	−	520.000i	0.399274	−	0.230521i
$173$	1367.45	+	789.500i	0.600957	+	0.346963i	0.769418	−	0.638746i	$-0.220546\pi$
$173$	1367.45	+	789.500i	0.600957	+	0.346963i	−0.168461	+	0.985708i	$0.553880\pi$
$174$	−212.000			−0.0923660
$175$		0			0
$176$	560.000			0.239839
$177$	−14.7224	−	8.50000i	−0.00625201	−	0.00360960i
$178$	−1512.08	+	873.000i	−0.636715	+	0.367607i
$179$	1225.50	+	2122.63i	0.511722	+	0.886328i	0.999908	+	0.0135883i	$0.00432541\pi$
$179$	1225.50	+	2122.63i	0.511722	+	0.886328i	−0.488186	+	0.872740i	$0.662341\pi$
$180$		0			0
$181$	−1170.00			−0.480472			−0.240236	−	0.970715i	$-0.577225\pi$
$181$	−1170.00			−0.480472			−0.240236	+	0.970715i	$0.577225\pi$
$182$	−2171.99	+	1122.00i	−0.884608	+	0.456968i
$183$			51.0000i			0.0206012i
$184$	28.0000	−	48.4974i	0.0112184	−	0.0194309i
$185$		0			0
$186$	−75.0000	−	129.904i	−0.0295660	−	0.0512097i
$187$	−1788.34	−	1032.50i	−0.699340	−	0.403764i
$188$			684.000i			0.265350i
$189$	530.000	−	826.188i	0.203978	−	0.317970i
$190$		0			0
$191$	637.500	−	1104.18i	0.241507	−	0.418303i	−0.719637	−	0.694351i	$-0.755692\pi$
$191$	637.500	−	1104.18i	0.241507	−	0.418303i	0.961144	+	0.276048i	$0.0890249\pi$
$192$	−55.4256	+	32.0000i	−0.0208333	+	0.0120281i
$193$	−30.3109	+	17.5000i	−0.0113048	+	0.00652683i	−0.505642	−	0.862744i	$-0.668744\pi$
$193$	−30.3109	+	17.5000i	−0.0113048	+	0.00652683i	0.494337	+	0.869270i	$0.335411\pi$
$194$	290.000	−	502.295i	0.107324	−	0.185890i
$195$		0			0
$196$	−794.000	+	1118.90i	−0.289359	+	0.407764i
$197$		−	2734.00i		−	0.988779i	−0.869241	−	0.494389i	$-0.835392\pi$
$197$		−	2734.00i		−	0.988779i	0.869241	−	0.494389i	$-0.164608\pi$
$198$	1576.17	+	910.000i	0.565724	+	0.326621i
$199$	1121.50	+	1942.49i	0.399503	+	0.691959i	0.993665	−	0.112387i	$-0.0358495\pi$
$199$	1121.50	+	1942.49i	0.399503	+	0.691959i	−0.594162	+	0.804345i	$0.702516\pi$
$200$		0			0
$201$	219.500	−	380.185i	0.0770265	−	0.133414i
$202$			2170.00i			0.755845i
$203$	1652.38	+	1060.00i	0.571301	+	0.366490i
$204$	236.000			0.0809966
$205$		0			0
$206$	1553.00	+	2689.87i	0.525256	+	0.909769i
$207$	157.617	−	91.0000i	0.0529232	−	0.0305553i
$208$	914.523	+	528.000i	0.304859	+	0.176011i
$209$	−4795.00			−1.58697
$210$		0			0
$211$	1172.00			0.382388			0.191194	−	0.981552i	$-0.438764\pi$
$211$	1172.00			0.382388			0.191194	+	0.981552i	$0.438764\pi$
$212$	1444.53	+	834.000i	0.467975	+	0.270186i
$213$	−678.964	+	392.000i	−0.218412	+	0.126100i
$214$	−129.000	−	223.435i	−0.0412068	−	0.0713723i
$215$		0			0
$216$	−424.000			−0.133563
$217$	−64.9519	+	1387.50i	−0.0203190	+	0.434054i
$218$		−	1930.00i		−	0.599615i
$219$	−147.500	+	255.477i	−0.0455120	+	0.0788291i
$220$		0			0
$221$	−1947.00	−	3372.30i	−0.592622	−	1.02645i
$222$	−19.0526	−	11.0000i	−0.00576002	−	0.00332555i
$223$		−	2024.00i		−	0.607790i	−0.952706	−	0.303895i	$-0.901713\pi$
$223$		−	2024.00i		−	0.607790i	0.952706	−	0.303895i	$-0.0982871\pi$
$224$	592.000	+	27.7128i	0.176583	+	0.00826625i
$225$		0			0
$226$	−50.0000	+	86.6025i	−0.0147166	+	0.0254899i
$227$	2226.55	−	1285.50i	0.651019	−	0.375866i	−0.137827	−	0.990456i	$-0.544012\pi$
$227$	2226.55	−	1285.50i	0.651019	−	0.375866i	0.788847	+	0.614590i	$0.210679\pi$
$228$	474.582	−	274.000i	0.137851	−	0.0795881i
$229$	447.500	−	775.093i	0.129134	−	0.223666i	−0.794207	−	0.607647i	$-0.792114\pi$
$229$	447.500	−	775.093i	0.129134	−	0.223666i	0.923341	+	0.383980i	$0.125447\pi$
$230$		0			0
$231$	297.500	+	575.907i	0.0847362	+	0.164034i
$232$		−	848.000i		−	0.239974i
$233$	1547.59	+	893.500i	0.435132	+	0.251224i	0.701531	−	0.712639i	$-0.252500\pi$
$233$	1547.59	+	893.500i	0.435132	+	0.251224i	−0.266398	+	0.963863i	$0.585834\pi$
$234$	1716.00	+	2972.20i	0.479395	+	0.830336i
$235$		0			0
$236$	34.0000	−	58.8897i	0.00937801	−	0.0162432i
$237$			495.000i			0.135670i
$238$	−1839.44	−	1180.00i	−0.500979	−	0.321378i
$239$	5100.00			1.38030			0.690150	−	0.723667i	$-0.257545\pi$
$239$	5100.00			1.38030			0.690150	+	0.723667i	$0.257545\pi$
$240$		0			0
$241$	2088.50	+	3617.39i	0.558225	+	0.966873i	0.997645	+	0.0685917i	$0.0218506\pi$
$241$	2088.50	+	3617.39i	0.558225	+	0.966873i	−0.439420	+	0.898282i	$0.644816\pi$
$242$	183.597	−	106.000i	0.0487690	−	0.0281568i
$243$	−1801.33	−	1040.00i	−0.475537	−	0.274552i
$244$	−204.000			−0.0535236
$245$		0			0
$246$	−996.000			−0.258141
$247$	−7830.60	−	4521.00i	−2.01720	−	1.16463i
$248$	519.615	−	300.000i	0.133047	−	0.0768146i
$249$	−466.000	−	807.136i	−0.118601	−	0.205422i
$250$		0			0
$251$	−4680.00			−1.17689			−0.588444	−	0.808538i	$-0.700259\pi$
$251$	−4680.00			−1.17689			−0.588444	+	0.808538i	$0.700259\pi$
$252$	1621.20	+	1040.00i	0.405262	+	0.259976i
$253$			245.000i			0.0608815i
$254$	−936.000	+	1621.20i	−0.231220	+	0.400485i
$255$		0			0
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	1514.68	+	874.500i	0.367638	+	0.212256i	0.672426	−	0.740164i	$-0.265252\pi$
$257$	1514.68	+	874.500i	0.367638	+	0.212256i	−0.304788	+	0.952420i	$0.598586\pi$
$258$		−	520.000i		−	0.125480i
$259$	93.5000	+	180.999i	0.0224317	+	0.0434237i
$260$		0			0
$261$	1378.00	−	2386.77i	0.326805	−	0.566043i
$262$	1307.70	−	755.000i	0.308358	−	0.178031i
$263$	3873.73	−	2236.50i	0.908230	−	0.524367i	0.0283689	−	0.999598i	$-0.490969\pi$
$263$	3873.73	−	2236.50i	0.908230	−	0.524367i	0.879861	+	0.475231i	$0.157635\pi$
$264$	140.000	−	242.487i	0.0326379	−	0.0565305i
$265$		0			0
$266$	−5069.00	−	237.291i	−1.16842	−	0.0546964i
$267$			873.000i			0.200100i
$268$	1520.74	+	878.000i	0.346619	+	0.200121i
$269$	987.500	+	1710.40i	0.223825	+	0.387676i	0.955966	−	0.293476i	$-0.0948122\pi$
$269$	987.500	+	1710.40i	0.223825	+	0.387676i	−0.732141	+	0.681153i	$0.761479\pi$
$270$		0			0
$271$	4219.50	−	7308.39i	0.945817	−	1.63820i	0.191710	−	0.981452i	$-0.438597\pi$
$271$	4219.50	−	7308.39i	0.945817	−	1.63820i	0.754107	−	0.656751i	$-0.228070\pi$
$272$			944.000i			0.210435i
$273$	−57.1577	+	1221.00i	−0.0126716	+	0.270690i
$274$	−4714.00			−1.03935
$275$		0			0
$276$	−14.0000	−	24.2487i	−0.00305326	−	0.00528841i
$277$	456.395	−	263.500i	0.0989969	−	0.0571559i	−0.449684	−	0.893188i	$-0.648463\pi$
$277$	456.395	−	263.500i	0.0989969	−	0.0571559i	0.548681	+	0.836032i	$0.315130\pi$
$278$	−48.4974	−	28.0000i	−0.0104629	−	0.00604075i
$279$	1950.00			0.418435
$280$		0			0
$281$	−202.000			−0.0428837			−0.0214418	−	0.999770i	$-0.506826\pi$
$281$	−202.000			−0.0428837			−0.0214418	+	0.999770i	$0.506826\pi$
$282$	296.181	+	171.000i	0.0625436	+	0.0361096i
$283$	6884.04	−	3974.50i	1.44598	−	0.834839i	0.447745	−	0.894161i	$-0.352227\pi$
$283$	6884.04	−	3974.50i	1.44598	−	0.834839i	0.998239	+	0.0593220i	$0.0188939\pi$
$284$	−1568.00	−	2715.86i	−0.327619	−	0.567452i
$285$		0			0
$286$	−4620.00			−0.955197
$287$	7763.05	+	4980.00i	1.59665	+	1.02425i
$288$		−	832.000i		−	0.170229i
$289$	−716.000	+	1240.15i	−0.145736	+	0.252422i
$290$		0			0
$291$	−145.000	−	251.147i	−0.0292098	−	0.0505929i
$292$	−1021.91	−	590.000i	−0.204804	−	0.118244i
$293$		−	318.000i		−	0.0634053i	−0.999497	−	0.0317027i	$-0.989907\pi$
$293$		−	318.000i		−	0.0634053i	0.999497	−	0.0317027i	$-0.0100930\pi$
$294$	286.000	+	623.538i	0.0567342	+	0.123692i
$295$		0			0
$296$	44.0000	−	76.2102i	0.00864003	−	0.0149650i
$297$	1606.48	−	927.500i	0.313863	−	0.181209i
$298$	3975.06	−	2295.00i	0.772714	−	0.446127i
$299$	−231.000	+	400.104i	−0.0446792	+	0.0773866i
$300$		0			0
$301$	−2600.00	+	4053.00i	−0.497879	+	0.776116i
$302$			2218.00i			0.422621i
$303$	939.638	+	542.500i	0.178154	+	0.102857i
$304$	1096.00	+	1898.33i	0.206776	+	0.358147i
$305$		0			0
$306$	−1534.00	+	2656.97i	−0.286578	+	0.496368i
$307$		−	8132.00i		−	1.51178i	−0.654696	−	0.755892i	$-0.727203\pi$
$307$		−	8132.00i		−	1.51178i	0.654696	−	0.755892i	$-0.272797\pi$
$308$	−2303.63	+	1190.00i	−0.426173	+	0.220151i
$309$	1553.00			0.285913
$310$		0			0
$311$	464.500	+	804.538i	0.0846925	+	0.146692i	0.905260	−	0.424858i	$-0.139676\pi$
$311$	464.500	+	804.538i	0.0846925	+	0.146692i	−0.820568	+	0.571549i	$0.806343\pi$
$312$	457.261	−	264.000i	0.0829722	−	0.0479040i
$313$	−180.999	−	104.500i	−0.0326859	−	0.0188712i	0.483568	−	0.875307i	$-0.339341\pi$
$313$	−180.999	−	104.500i	−0.0326859	−	0.0188712i	−0.516254	+	0.856436i	$0.672674\pi$
$314$	3118.00			0.560379
$315$		0			0
$316$	−1980.00			−0.352480
$317$	−6175.63	−	3565.50i	−1.09419	−	0.631730i	−0.159500	−	0.987198i	$-0.550988\pi$
$317$	−6175.63	−	3565.50i	−1.09419	−	0.631730i	−0.934689	+	0.355468i	$0.884322\pi$
$318$	722.265	−	417.000i	0.127367	−	0.0735352i
$319$	1855.00	+	3212.95i	0.325580	+	0.563921i
$320$		0			0
$321$	−129.000			−0.0224301
$322$	−12.1244	+	259.000i	−0.00209834	+	0.0448246i
$323$		−	8083.00i		−	1.39242i
$324$	1298.00	−	2248.20i	0.222565	−	0.385494i
$325$		0			0
$326$	−2251.00	−	3898.85i	−0.382427	−	0.662384i
$327$	−835.715	−	482.500i	−0.141331	−	0.0815973i
$328$		−	3984.00i		−	0.670670i
$329$	−1453.50	−	2813.72i	−0.243569	−	0.471505i
$330$		0			0
$331$	3285.50	−	5690.65i	0.545581	−	0.944975i	−0.452989	−	0.891516i	$-0.649642\pi$
$331$	3285.50	−	5690.65i	0.545581	−	0.944975i	0.998570	−	0.0534583i	$-0.0170244\pi$
$332$	3228.54	−	1864.00i	0.533703	−	0.308133i
$333$	247.683	−	143.000i	0.0407596	−	0.0235326i
$334$	−2788.00	+	4828.96i	−0.456744	+	0.791104i
$335$		0			0
$336$	160.000	−	249.415i	0.0259783	−	0.0404962i
$337$		−	11466.0i		−	1.85339i	−0.375813	−	0.926696i	$-0.622636\pi$
$337$		−	11466.0i		−	1.85339i	0.375813	−	0.926696i	$-0.377364\pi$
$338$	−3739.50	−	2159.00i	−0.601781	−	0.347438i
$339$	25.0000	+	43.3013i	0.00400535	+	0.00693747i
$340$		0			0
$341$	−1312.50	+	2273.32i	−0.208434	+	0.361018i
$342$			7124.00i			1.12638i
$343$	888.542	−	6290.00i	0.139874	−	0.990169i
$344$	2080.00			0.326006
$345$		0			0
$346$	1579.00	+	2734.91i	0.245340	+	0.424941i
$347$	−8467.13	+	4888.50i	−1.30991	+	0.756278i	−0.982081	−	0.188459i	$-0.939651\pi$
$347$	−8467.13	+	4888.50i	−1.30991	+	0.756278i	−0.327831	+	0.944737i	$0.606318\pi$
$348$	−367.195	−	212.000i	−0.0565624	−	0.0326563i
$349$	−11914.0			−1.82734			−0.913670	−	0.406456i	$-0.866764\pi$
$349$	−11914.0			−1.82734			−0.913670	+	0.406456i	$0.866764\pi$
$350$		0			0
$351$	3498.00			0.531936
$352$	969.948	+	560.000i	0.146871	+	0.0847957i
$353$	−7900.75	+	4561.50i	−1.19126	+	0.687774i	−0.958592	−	0.284783i	$-0.908079\pi$
$353$	−7900.75	+	4561.50i	−1.19126	+	0.687774i	−0.232667	+	0.972556i	$0.574745\pi$
$354$	−17.0000	−	29.4449i	−0.00255237	−	0.00442084i
$355$		0			0
$356$	−3492.00			−0.519875
$357$	−970.814	+	501.500i	−0.143924	+	0.0743479i
$358$			4902.00i			0.723684i
$359$	4074.50	−	7057.24i	0.599008	−	1.03751i	−0.393960	−	0.919128i	$-0.628895\pi$
$359$	4074.50	−	7057.24i	0.599008	−	1.03751i	0.992968	−	0.118385i	$-0.0377716\pi$
$360$		0			0
$361$	−5955.00	−	10314.4i	−0.868202	−	1.50377i
$362$	−2026.50	−	1170.00i	−0.294228	−	0.169872i
$363$		−	106.000i		−	0.0153266i
$364$	−4884.00	−	228.631i	−0.703272	−	0.0329217i
$365$		0			0
$366$	−51.0000	+	88.3346i	−0.00728364	+	0.0126156i
$367$	8375.33	−	4835.50i	1.19125	−	0.687769i	0.232660	−	0.972558i	$-0.425257\pi$
$367$	8375.33	−	4835.50i	1.19125	−	0.687769i	0.958590	+	0.284790i	$0.0919237\pi$
$368$	96.9948	−	56.0000i	0.0137397	−	0.00793261i
$369$	6474.00	−	11213.3i	0.913341	−	1.58195i
$370$		0			0
$371$	−7714.50	−	361.133i	−1.07956	−	0.0505366i
$372$		−	300.000i		−	0.0418126i
$373$	−3558.50	−	2054.50i	−0.493973	−	0.285196i	0.232248	−	0.972657i	$-0.425392\pi$
$373$	−3558.50	−	2054.50i	−0.493973	−	0.285196i	−0.726221	+	0.687461i	$0.758725\pi$
$374$	−2065.00	−	3576.68i	−0.285504	−	0.494508i
$375$		0			0
$376$	−684.000	+	1184.72i	−0.0938154	+	0.162493i
$377$			6996.00i			0.955736i
$378$	1744.18	−	901.000i	0.237330	−	0.122599i
$379$	3488.00			0.472735			0.236367	−	0.971664i	$-0.424043\pi$
$379$	3488.00			0.472735			0.236367	+	0.971664i	$0.424043\pi$
$380$		0			0
$381$	468.000	+	810.600i	0.0629301	+	0.108998i
$382$	2208.36	−	1275.00i	0.295785	−	0.170771i
$383$	7549.14	+	4358.50i	1.00716	+	0.581485i	0.910360	−	0.413818i	$-0.135805\pi$
$383$	7549.14	+	4358.50i	1.00716	+	0.581485i	0.0968028	+	0.995304i	$0.469138\pi$
$384$	−128.000			−0.0170103
$385$		0			0
$386$	−70.0000			−0.00923033
$387$	5854.33	+	3380.00i	0.768973	+	0.443967i
$388$	1004.59	−	580.000i	0.131444	−	0.0758893i
$389$	81.5000	+	141.162i	0.0106227	+	0.0183990i	0.871288	−	0.490772i	$-0.163285\pi$
$389$	81.5000	+	141.162i	0.0106227	+	0.0183990i	−0.860665	+	0.509171i	$0.829952\pi$
$390$		0			0
$391$	−413.000			−0.0534177
$392$	−2494.15	+	1144.00i	−0.321362	+	0.147400i
$393$		−	755.000i		−	0.0969077i
$394$	2734.00	−	4735.43i	0.349586	−	0.605501i
$395$		0			0
$396$	1820.00	+	3152.33i	0.230956	+	0.400027i
$397$	−865.159	−	499.500i	−0.109373	−	0.0631466i	0.444316	−	0.895870i	$-0.353447\pi$
$397$	−865.159	−	499.500i	−0.109373	−	0.0631466i	−0.553689	+	0.832724i	$0.686780\pi$
$398$			4486.00i			0.564982i
$399$	−1370.00	+	2135.62i	−0.171894	+	0.267957i
$400$		0			0
$401$	7378.50	−	12779.9i	0.918865	−	1.59152i	0.117722	−	0.993047i	$-0.462441\pi$
$401$	7378.50	−	12779.9i	0.918865	−	1.59152i	0.801143	−	0.598474i	$-0.204226\pi$
$402$	760.370	−	439.000i	0.0943379	−	0.0544660i
$403$	−4286.83	+	2475.00i	−0.529881	+	0.305927i
$404$	−2170.00	+	3758.55i	−0.267232	+	0.462859i
$405$		0			0
$406$	1802.00	+	3488.35i	0.220275	+	0.426414i
$407$			385.000i			0.0468888i
$408$	408.764	+	236.000i	0.0496001	+	0.0286366i
$409$	−66.5000	−	115.181i	−0.00803964	−	0.0139251i	0.861978	−	0.506946i	$-0.169226\pi$
$409$	−66.5000	−	115.181i	−0.00803964	−	0.0139251i	−0.870017	+	0.493021i	$0.835892\pi$
$410$		0			0
$411$	−1178.50	+	2041.22i	−0.141438	+	0.244978i
$412$			6212.00i			0.742823i
$413$	−14.7224	+	314.500i	−0.00175410	+	0.0374710i
$414$	364.000			0.0432117
$415$		0			0
$416$	1056.00	+	1829.05i	0.124458	+	0.215568i
$417$	−24.2487	+	14.0000i	−0.00284764	+	0.00164408i
$418$	−8305.18	−	4795.00i	−0.971818	−	0.561079i
$419$	6420.00			0.748538			0.374269	−	0.927320i	$-0.377894\pi$
$419$	6420.00			0.748538			0.374269	+	0.927320i	$0.377894\pi$
$420$		0			0
$421$	10266.0			1.18844			0.594221	−	0.804302i	$-0.297460\pi$
$421$	10266.0			1.18844			0.594221	+	0.804302i	$0.297460\pi$
$422$	2029.96	+	1172.00i	0.234164	+	0.135194i
$423$	−3850.35	+	2223.00i	−0.442578	+	0.255522i
$424$	1668.00	+	2889.06i	0.191050	+	0.330908i
$425$		0			0
$426$	−1568.00			−0.178333
$427$	839.179	−	433.500i	0.0951070	−	0.0491301i
$428$		−	516.000i		−	0.0582752i
$429$	−1155.00	+	2000.52i	−0.129986	+	0.225142i
$430$		0			0
$431$	7606.50	+	13174.8i	0.850098	+	1.47241i	0.881119	+	0.472894i	$0.156791\pi$
$431$	7606.50	+	13174.8i	0.850098	+	1.47241i	−0.0310213	+	0.999519i	$0.509876\pi$
$432$	−734.390	−	424.000i	−0.0817901	−	0.0472215i
$433$			1378.00i			0.152939i	0.997072	+	0.0764693i	$0.0243647\pi$
$433$			1378.00i			0.152939i	−0.997072	+	0.0764693i	$0.975635\pi$
$434$	−1500.00	+	2338.27i	−0.165904	+	0.258619i
$435$		0			0
$436$	1930.00	−	3342.86i	0.211996	−	0.367188i
$437$	−830.518	+	479.500i	−0.0909132	+	0.0524888i
$438$	−510.955	+	295.000i	−0.0557406	+	0.0321818i
$439$	−1381.50	+	2392.83i	−0.150195	+	0.260145i	−0.931299	−	0.364256i	$-0.881323\pi$
$439$	−1381.50	+	2392.83i	−0.150195	+	0.260145i	0.781104	+	0.624401i	$0.214657\pi$
$440$		0			0
$441$	−8879.00	−	833.116i	−0.958752	−	0.0899597i
$442$		−	7788.00i		−	0.838094i
$443$	5065.38	+	2924.50i	0.543259	+	0.313651i	0.746399	−	0.665499i	$-0.231781\pi$
$443$	5065.38	+	2924.50i	0.543259	+	0.313651i	−0.203140	+	0.979150i	$0.565115\pi$
$444$	−22.0000	−	38.1051i	−0.00235152	−	0.00407295i
$445$		0			0
$446$	2024.00	−	3505.67i	0.214886	−	0.372194i
$447$		−	2295.00i		−	0.242841i
$448$	997.661	+	640.000i	0.105212	+	0.0674937i
$449$	−4582.00			−0.481599			−0.240799	−	0.970575i	$-0.577410\pi$
$449$	−4582.00			−0.481599			−0.240799	+	0.970575i	$0.577410\pi$
$450$		0			0
$451$	8715.00	+	15094.8i	0.909919	+	1.57603i
$452$	−173.205	+	100.000i	−0.0180241	+	0.0104062i
$453$	960.422	+	554.500i	0.0996127	+	0.0575114i
$454$	5142.00			0.531555
$455$		0			0
$456$	1096.00			0.112555
$457$	−10003.5	−	5775.50i	−1.02394	−	0.591174i	−0.108700	−	0.994075i	$-0.534669\pi$
$457$	−10003.5	−	5775.50i	−1.02394	−	0.591174i	−0.915244	+	0.402901i	$0.868002\pi$
$458$	1550.19	−	895.000i	0.158156	−	0.0913114i
$459$	1563.50	+	2708.06i	0.158993	+	0.275384i
$460$		0			0
$461$	−9494.00			−0.959175			−0.479587	−	0.877494i	$-0.659214\pi$
$461$	−9494.00			−0.959175			−0.479587	+	0.877494i	$0.659214\pi$
$462$	−60.6218	+	1295.00i	−0.00610472	+	0.130409i
$463$			10160.0i			1.01982i	0.860229	+	0.509908i	$0.170321\pi$
$463$			10160.0i			1.01982i	−0.860229	+	0.509908i	$0.829679\pi$
$464$	848.000	−	1468.78i	0.0848436	−	0.146953i
$465$		0			0
$466$	1787.00	+	3095.17i	0.177642	+	0.307685i
$467$	1131.90	+	653.500i	0.112158	+	0.0647545i	0.555030	−	0.831831i	$-0.312707\pi$
$467$	1131.90	+	653.500i	0.112158	+	0.0647545i	−0.442872	+	0.896585i	$0.646040\pi$
$468$			6864.00i			0.677967i
$469$	−8121.50	−	380.185i	−0.799608	−	0.0374314i
$470$		0			0
$471$	779.500	−	1350.13i	0.0762579	−	0.132083i
$472$	117.779	−	68.0000i	0.0114857	−	0.00663126i
$473$	−7880.83	+	4550.00i	−0.766091	+	0.442303i
$474$	−495.000	+	857.365i	−0.0479665	+	0.0830803i
$475$		0			0
$476$	−2006.00	−	3883.26i	−0.193161	−	0.373926i
$477$			10842.0i			1.04072i
$478$	8833.46	+	5100.00i	0.845257	+	0.488010i
$479$	9143.50	+	15837.0i	0.872186	+	1.51067i	0.859730	+	0.510748i	$0.170632\pi$
$479$	9143.50	+	15837.0i	0.872186	+	1.51067i	0.0124559	+	0.999922i	$0.496035\pi$
$480$		0			0
$481$	−363.000	+	628.734i	−0.0344103	+	0.0596005i
$482$			8354.00i			0.789449i
$483$	109.119	+	70.0000i	0.0102797	+	0.00659443i
$484$	424.000			0.0398197
$485$		0			0
$486$	−2080.00	−	3602.67i	−0.194137	−	0.336256i
$487$	−12949.7	+	7476.50i	−1.20494	+	0.695673i	−0.961650	−	0.274281i	$-0.911560\pi$
$487$	−12949.7	+	7476.50i	−1.20494	+	0.695673i	−0.243291	+	0.969953i	$0.578227\pi$
$488$	−353.338	−	204.000i	−0.0327764	−	0.0189235i
$489$	−2251.00			−0.208167
$490$		0			0
$491$	14352.0			1.31914			0.659569	−	0.751644i	$-0.270739\pi$
$491$	14352.0			1.31914			0.659569	+	0.751644i	$0.270739\pi$
$492$	−1725.12	−	996.000i	−0.158078	−	0.0912666i
$493$	−5416.12	+	3127.00i	−0.494787	+	0.285665i
$494$	−9042.00	−	15661.2i	−0.823520	−	1.42638i
$495$		0			0
$496$	1200.00			0.108632
$497$	12221.4	+	7840.00i	1.10302	+	0.707590i
$498$		−	1864.00i		−	0.167727i
$499$	−2765.50	+	4789.99i	−0.248098	+	0.429718i	−0.962998	−	0.269509i	$-0.913139\pi$
$499$	−2765.50	+	4789.99i	−0.248098	+	0.429718i	0.714900	+	0.699226i	$0.246472\pi$
$500$		0			0
$501$	1394.00	+	2414.48i	0.124310	+	0.215311i
$502$	−8106.00	−	4680.00i	−0.720694	−	0.416093i
$503$		−	8400.00i		−	0.744607i	−0.928111	−	0.372304i	$-0.878568\pi$
$503$		−	8400.00i		−	0.744607i	0.928111	−	0.372304i	$-0.121432\pi$
$504$	1768.00	+	3422.53i	0.156256	+	0.302484i
$505$		0			0
$506$	−245.000	+	424.352i	−0.0215249	+	0.0372821i
$507$	−1869.75	+	1079.50i	−0.163784	+	0.0945607i
$508$	−3242.40	+	1872.00i	−0.283185	+	0.163497i
$509$	−1192.50	+	2065.47i	−0.103844	+	0.179863i	−0.913265	−	0.407365i	$-0.866448\pi$
$509$	−1192.50	+	2065.47i	−0.103844	+	0.179863i	0.809421	+	0.587228i	$0.199781\pi$
$510$		0			0
$511$	5457.50	+	255.477i	0.472457	+	0.0221167i
$512$		−	512.000i		−	0.0441942i
$513$	6288.21	+	3630.50i	0.541192	+	0.312457i
$514$	1749.00	+	3029.36i	0.150088	+	0.259960i
$515$		0			0
$516$	520.000	−	900.666i	0.0443638	−	0.0768404i
$517$		−	5985.00i		−	0.509130i
$518$	−19.0526	+	407.000i	−0.00161606	+	0.0345223i
$519$	1579.00			0.133546
$520$		0			0
$521$	4576.50	+	7926.73i	0.384837	+	0.666557i	0.991747	−	0.128214i	$-0.0409243\pi$
$521$	4576.50	+	7926.73i	0.384837	+	0.666557i	−0.606910	+	0.794771i	$0.707591\pi$
$522$	4773.53	−	2756.00i	0.400253	−	0.231086i
$523$	−11957.2	−	6903.50i	−0.999718	−	0.577187i	−0.0915530	−	0.995800i	$-0.529183\pi$
$523$	−11957.2	−	6903.50i	−0.999718	−	0.577187i	−0.908165	+	0.418613i	$0.862516\pi$
$524$	3020.00			0.251773
$525$		0			0
$526$	8946.00			0.741567
$527$	−3832.16	−	2212.50i	−0.316758	−	0.182880i
$528$	484.974	−	280.000i	0.0399731	−	0.0230785i
$529$	−6059.00	−	10494.5i	−0.497986	−	0.862538i
$530$		0			0
$531$	442.000			0.0361227
$532$	−8542.47	−	5480.00i	−0.696172	−	0.446594i
$533$			32868.0i			2.67105i
$534$	−873.000	+	1512.08i	−0.0707461	+	0.122536i
$535$		0			0
$536$	1756.00	+	3041.48i	0.141507	+	0.245097i
$537$	2122.63	+	1225.50i	0.170574	+	0.0984809i
$538$			3950.00i			0.316536i
$539$	6947.50	−	9790.42i	0.555195	−	0.782381i
$540$		0			0
$541$	−4087.50	+	7079.76i	−0.324834	+	0.562629i	−0.981479	−	0.191571i	$-0.938642\pi$
$541$	−4087.50	+	7079.76i	−0.324834	+	0.562629i	0.656645	+	0.754200i	$0.271975\pi$
$542$	14616.8	−	8439.00i	1.15838	−	0.668794i
$543$	−1013.25	+	585.000i	−0.0800787	+	0.0462334i
$544$	−944.000	+	1635.06i	−0.0744001	+	0.128865i
$545$		0			0
$546$	−1320.00	+	2057.68i	−0.103463	+	0.161283i
$547$			4656.00i			0.363942i	0.983304	+	0.181971i	$0.0582477\pi$
$547$			4656.00i			0.363942i	−0.983304	+	0.181971i	$0.941752\pi$
$548$	−8164.89	−	4714.00i	−0.636472	−	0.367467i
$549$	−663.000	−	1148.35i	−0.0515413	−	0.0892721i
$550$		0			0
$551$	−7261.00	+	12576.4i	−0.561396	+	0.972366i
$552$		−	56.0000i		−	0.00431797i
$553$	8144.97	−	4207.50i	0.626328	−	0.323546i
$554$	1054.00			0.0808306
$555$		0			0
$556$	−56.0000	−	96.9948i	−0.00427146	−	0.00739838i
$557$	6064.78	−	3501.50i	0.461352	−	0.266361i	−0.251261	−	0.967919i	$-0.580845\pi$
$557$	6064.78	−	3501.50i	0.461352	−	0.266361i	0.712612	+	0.701558i	$0.247512\pi$
$558$	3377.50	+	1950.00i	0.256238	+	0.147939i
$559$	−17160.0			−1.29837
$560$		0			0
$561$	−2065.00			−0.155409
$562$	−349.874	−	202.000i	−0.0262608	−	0.0151617i
$563$	17106.6	−	9876.50i	1.28056	−	0.739334i	0.303612	−	0.952796i	$-0.401807\pi$
$563$	17106.6	−	9876.50i	1.28056	−	0.739334i	0.976951	+	0.213462i	$0.0684740\pi$
$564$	342.000	+	592.361i	0.0255333	+	0.0442250i
$565$		0			0
$566$	15898.0			1.18064
$567$	−562.050	+	12006.5i	−0.0416295	+	0.889287i
$568$		−	6272.00i		−	0.463323i
$569$	−3448.50	+	5972.98i	−0.254075	+	0.440071i	−0.964644	−	0.263557i	$-0.915104\pi$
$569$	−3448.50	+	5972.98i	−0.254075	+	0.440071i	0.710569	+	0.703628i	$0.248438\pi$
$570$		0			0
$571$	−12457.5	−	21577.0i	−0.913013	−	1.58138i	−0.809785	−	0.586726i	$-0.800416\pi$
$571$	−12457.5	−	21577.0i	−0.913013	−	1.58138i	−0.103227	−	0.994658i	$-0.532917\pi$
$572$	−8002.07	−	4620.00i	−0.584936	−	0.337713i
$573$		−	1275.00i		−	0.0929562i
$574$	8466.00	+	16388.7i	0.615617	+	1.19172i
$575$		0			0
$576$	832.000	−	1441.07i	0.0601852	−	0.104244i
$577$	109.985	−	63.5000i	0.00793543	−	0.00458152i	−0.496027	−	0.868307i	$-0.665208\pi$
$577$	109.985	−	63.5000i	0.00793543	−	0.00458152i	0.503962	+	0.863726i	$0.331875\pi$
$578$	−2480.30	+	1432.00i	−0.178489	+	0.103051i
$579$	−17.5000	+	30.3109i	−0.00125609	+	0.00217561i
$580$		0			0
$581$	−9320.00	+	14528.4i	−0.665506	+	1.03742i
$582$		−	580.000i		−	0.0413089i
$583$	−12639.6	−	7297.50i	−0.897908	−	0.518407i
$584$	−1180.00	−	2043.82i	−0.0836109	−	0.144818i
$585$		0			0
$586$	318.000	−	550.792i	0.0224172	−	0.0388277i
$587$			9044.00i			0.635921i	0.948104	+	0.317961i	$0.102998\pi$
$587$			9044.00i			0.635921i	−0.948104	+	0.317961i	$0.897002\pi$
$588$	−128.172	+	1366.00i	−0.00898931	+	0.0958042i
$589$	−10275.0			−0.718801
$590$		0			0
$591$	−1367.00	−	2367.71i	−0.0951453	−	0.164796i
$592$	152.420	−	88.0000i	0.0105818	−	0.00610942i
$593$	−9267.34	−	5350.50i	−0.641760	−	0.370521i	0.143532	−	0.989646i	$-0.454154\pi$
$593$	−9267.34	−	5350.50i	−0.641760	−	0.370521i	−0.785292	+	0.619125i	$0.787487\pi$
$594$	3710.00			0.256268
$595$		0			0
$596$	9180.00			0.630919
$597$	1942.49	+	1121.50i	0.133168	+	0.0768843i
$598$	−800.207	+	462.000i	−0.0547206	+	0.0315930i
$599$	10399.5	+	18012.5i	0.709369	+	1.22866i	0.965091	+	0.261913i	$0.0843533\pi$
$599$	10399.5	+	18012.5i	0.709369	+	1.22866i	−0.255722	+	0.966750i	$0.582313\pi$
$600$		0			0
$601$	−1402.00			−0.0951560			−0.0475780	−	0.998868i	$-0.515150\pi$
$601$	−1402.00			−0.0951560			−0.0475780	+	0.998868i	$0.515150\pi$
$602$	−8556.33	+	4420.00i	−0.579286	+	0.299245i
$603$			11414.0i			0.770836i
$604$	−2218.00	+	3841.69i	−0.149419	+	0.258801i
$605$		0			0
$606$	1085.00	+	1879.28i	0.0727312	+	0.125974i
$607$	−5650.82	−	3262.50i	−0.377858	−	0.218156i	0.299028	−	0.954244i	$-0.403338\pi$
$607$	−5650.82	−	3262.50i	−0.377858	−	0.218156i	−0.676886	+	0.736088i	$0.736671\pi$
$608$			4384.00i			0.292425i
$609$	1961.00	+	91.7987i	0.130482	+	0.00610816i
$610$		0			0
$611$	5643.00	−	9773.96i	0.373636	−	0.647156i
$612$	−5313.93	+	3068.00i	−0.350985	+	0.202641i
$613$	−13034.5	+	7525.50i	−0.858826	+	0.495844i	−0.863619	−	0.504145i	$-0.831808\pi$
$613$	−13034.5	+	7525.50i	−0.858826	+	0.495844i	0.00479285	+	0.999989i	$0.498474\pi$
$614$	8132.00	−	14085.0i	0.534496	−	0.925775i
$615$		0			0
$616$	−5180.00	−	242.487i	−0.338812	−	0.0158605i
$617$			11150.0i			0.727524i	0.931492	+	0.363762i	$0.118508\pi$
$617$			11150.0i			0.727524i	−0.931492	+	0.363762i	$0.881492\pi$
$618$	2689.87	+	1553.00i	0.175085	+	0.101085i
$619$	1707.50	+	2957.48i	0.110873	+	0.192037i	0.916122	−	0.400899i	$-0.131302\pi$
$619$	1707.50	+	2957.48i	0.110873	+	0.192037i	−0.805250	+	0.592936i	$0.797969\pi$
$620$		0			0
$621$	185.500	−	321.295i	0.0119869	−	0.0207619i
$622$			1858.00i			0.119773i
$623$	14364.8	−	7420.50i	0.923775	−	0.477201i
$624$	1056.00			0.0677465
$625$		0			0
$626$	−209.000	−	361.999i	−0.0133440	−	0.0231124i
$627$	−4152.59	+	2397.50i	−0.264495	+	0.152706i
$628$	5400.53	+	3118.00i	0.343160	+	0.198124i
$629$	−649.000			−0.0411404
$630$		0			0
$631$	−21184.0			−1.33648			−0.668242	−	0.743944i	$-0.732953\pi$
$631$	−21184.0			−1.33648			−0.668242	+	0.743944i	$0.732953\pi$
$632$	−3429.46	−	1980.00i	−0.215849	−	0.124621i
$633$	1014.98	−	586.000i	0.0637313	−	0.0367953i
$634$	−7131.00	−	12351.3i	−0.446701	−	0.773708i
$635$		0			0
$636$	1668.00			0.103995
$637$	20576.8	−	9438.00i	1.27988	−	0.587044i
$638$			7420.00i			0.460440i
$639$	10192.0	−	17653.1i	0.630969	−	1.09287i
$640$		0			0
$641$	5352.50	+	9270.80i	0.329814	+	0.571255i	0.982475	−	0.186395i	$-0.0596805\pi$
$641$	5352.50	+	9270.80i	0.329814	+	0.571255i	−0.652660	+	0.757651i	$0.726347\pi$
$642$	−223.435	−	129.000i	−0.0137356	−	0.00793026i
$643$		−	6860.00i		−	0.420734i	−0.977622	−	0.210367i	$-0.932534\pi$
$643$		−	6860.00i		−	0.420734i	0.977622	−	0.210367i	$-0.0674659\pi$
$644$	−280.000	+	436.477i	−0.0171328	+	0.0267074i
$645$		0			0
$646$	8083.00	−	14000.2i	0.492293	−	0.852677i
$647$	12525.3	−	7231.50i	0.761084	−	0.439412i	−0.0686008	−	0.997644i	$-0.521853\pi$
$647$	12525.3	−	7231.50i	0.761084	−	0.439412i	0.829685	+	0.558232i	$0.188520\pi$
$648$	4496.40	−	2596.00i	0.272586	−	0.157377i
$649$	−297.500	+	515.285i	−0.0179937	+	0.0311660i
$650$		0			0
$651$	637.500	+	1234.09i	0.0383803	+	0.0742975i
$652$		−	9004.00i		−	0.540834i
$653$	5177.97	+	2989.50i	0.310305	+	0.179155i	0.647063	−	0.762436i	$-0.275997\pi$
$653$	5177.97	+	2989.50i	0.310305	+	0.179155i	−0.336758	+	0.941591i	$0.609330\pi$
$654$	−965.000	−	1671.43i	−0.0576980	−	0.0999359i
$655$		0			0
$656$	3984.00	−	6900.49i	0.237117	−	0.410700i
$657$		−	7670.00i		−	0.455457i
$658$	296.181	−	6327.00i	0.0175476	−	0.374851i
$659$	6940.00			0.410234			0.205117	−	0.978737i	$-0.434243\pi$
$659$	6940.00			0.410234			0.205117	+	0.978737i	$0.434243\pi$
$660$		0			0
$661$	−6699.50	−	11603.9i	−0.394221	−	0.682812i	0.598780	−	0.800914i	$-0.295652\pi$
$661$	−6699.50	−	11603.9i	−0.394221	−	0.682812i	−0.993001	+	0.118102i	$0.962319\pi$
$662$	11381.3	−	6571.00i	0.668198	−	0.385784i
$663$	−3372.30	−	1947.00i	−0.197541	−	0.114050i
$664$	7456.00			0.435766
$665$		0			0
$666$	572.000			0.0332801
$667$	642.591	+	371.000i	0.0373032	+	0.0215370i
$668$	−9657.92	+	5576.00i	−0.559395	+	0.322967i
$669$	−1012.00	−	1752.84i	−0.0584846	−	0.101298i
$670$		0			0
$671$	1785.00			0.102696
$672$	526.543	−	272.000i	0.0302260	−	0.0156140i
$673$		−	29510.0i		−	1.69023i	−0.534582	−	0.845117i	$-0.679531\pi$
$673$		−	29510.0i		−	1.69023i	0.534582	−	0.845117i	$-0.320469\pi$
$674$	11466.0	−	19859.7i	0.655273	−	1.13497i
$675$		0			0
$676$	−4318.00	−	7479.00i	−0.245676	−	0.425523i
$677$	22517.5	+	13000.5i	1.27831	+	0.738035i	0.976538	−	0.215344i	$-0.0690872\pi$
$677$	22517.5	+	13000.5i	1.27831	+	0.738035i	0.301776	+	0.953379i	$0.402421\pi$
$678$			100.000i			0.00566442i
$679$	−2900.00	+	4520.65i	−0.163905	+	0.255503i
$680$		0			0
$681$	1285.50	−	2226.55i	0.0723355	−	0.125289i
$682$	−4546.63	+	2625.00i	−0.255278	+	0.147385i
$683$	7625.35	−	4402.50i	0.427198	−	0.246643i	−0.270954	−	0.962592i	$-0.587339\pi$
$683$	7625.35	−	4402.50i	0.427198	−	0.246643i	0.698152	+	0.715949i	$0.254006\pi$
$684$	−7124.00	+	12339.1i	−0.398235	+	0.689764i
$685$		0			0
$686$	7829.00	−	10006.1i	0.435733	−	0.556899i
$687$		−	895.000i		−	0.0497036i
$688$	3602.67	+	2080.00i	0.199637	+	0.115261i
$689$	−13761.0	−	23834.8i	−0.760889	−	1.31790i
$690$		0			0
$691$	−14342.5	+	24841.9i	−0.789601	+	1.36763i	0.136610	+	0.990625i	$0.456379\pi$
$691$	−14342.5	+	24841.9i	−0.789601	+	1.36763i	−0.926211	+	0.377004i	$0.876954\pi$
$692$			6316.00i			0.346963i
$693$	−14185.5	−	9100.00i	−0.777579	−	0.498817i
$694$	−19554.0			−1.06954
$695$		0			0
$696$	−424.000	−	734.390i	−0.0230915	−	0.0399956i
$697$	−25445.6	+	14691.0i	−1.38281	+	0.798366i
$698$	−20635.7	−	11914.0i	−1.11901	−	0.646062i
$699$	1787.00			0.0966961
$700$		0			0
$701$	−3146.00			−0.169505			−0.0847523	−	0.996402i	$-0.527010\pi$
$701$	−3146.00			−0.169505			−0.0847523	+	0.996402i	$0.527010\pi$
$702$	6058.71	+	3498.00i	0.325743	+	0.188068i
$703$	−1305.10	+	753.500i	−0.0700182	+	0.0404250i
$704$	1120.00	+	1939.90i	0.0599596	+	0.103853i
$705$		0			0
$706$	−18246.0			−0.972659
$707$	939.638	−	20072.5i	0.0499840	−	1.06776i
$708$		−	68.0000i		−	0.00360960i
$709$	629.500	−	1090.33i	0.0333447	−	0.0577547i	−0.848871	−	0.528599i	$-0.822717\pi$
$709$	629.500	−	1090.33i	0.0333447	−	0.0577547i	0.882216	+	0.470845i	$0.156051\pi$
$710$		0			0
$711$	−6435.00	−	11145.7i	−0.339425	−	0.587902i
$712$	−6048.32	−	3492.00i	−0.318357	−	0.183804i
$713$			525.000i			0.0275756i
$714$	−2183.00	−	102.191i	−0.114421	−	0.00535631i
$715$		0			0
$716$	−4902.00	+	8490.51i	−0.255861	+	0.443164i
$717$	4416.73	−	2550.00i	0.230050	−	0.132819i
$718$	14114.5	−	8149.00i	0.733632	−	0.423563i
$719$	8212.50	−	14224.5i	0.425973	−	0.737807i	−0.570538	−	0.821271i	$-0.693265\pi$
$719$	8212.50	−	14224.5i	0.425973	−	0.737807i	0.996511	+	0.0834645i	$0.0265985\pi$
$720$		0			0
$721$	−13200.5	−	25553.8i	−0.681848	−	1.31994i
$722$		−	23820.0i		−	1.22782i
$723$	3617.39	+	2088.50i	0.186075	+	0.107430i
$724$	−2340.00	−	4053.00i	−0.120118	−	0.208050i
$725$		0			0
$726$	106.000	−	183.597i	0.00541877	−	0.00938559i
$727$		−	6032.00i		−	0.307723i	−0.988092	−	0.153861i	$-0.950829\pi$
$727$		−	6032.00i		−	0.307723i	0.988092	−	0.153861i	$-0.0491709\pi$
$728$	−8230.71	−	5280.00i	−0.419025	−	0.268805i
$729$	15443.0			0.784586
$730$		0			0
$731$	−7670.00	−	13284.8i	−0.388078	−	0.672171i
$732$	−176.669	+	102.000i	−0.00892060	+	0.00515031i
$733$	13200.8	+	7621.50i	0.665189	+	0.384047i	0.794251	−	0.607589i	$-0.207863\pi$
$733$	13200.8	+	7621.50i	0.665189	+	0.384047i	−0.129062	+	0.991636i	$0.541197\pi$
$734$	19342.0			0.972652
$735$		0			0
$736$	224.000			0.0112184
$737$	−13306.5	−	7682.50i	−0.665062	−	0.383974i
$738$	22426.6	−	12948.0i	1.11861	−	0.645830i
$739$	−5026.50	−	8706.15i	−0.250207	−	0.433371i	0.713376	−	0.700782i	$-0.247165\pi$
$739$	−5026.50	−	8706.15i	−0.250207	−	0.433371i	−0.963583	+	0.267411i	$0.913832\pi$
$740$		0			0
$741$	−9042.00			−0.448267
$742$	−13000.8	−	8340.00i	−0.643226	−	0.412629i
$743$		−	24384.0i		−	1.20399i	−0.798501	−	0.601993i	$-0.794373\pi$
$743$		−	24384.0i		−	1.20399i	0.798501	−	0.601993i	$-0.205627\pi$
$744$	300.000	−	519.615i	0.0147830	−	0.0256049i
$745$		0			0
$746$	−4109.00	−	7117.00i	−0.201664	−	0.349292i
$747$	20985.5	+	12116.0i	1.02787	+	0.593442i
$748$		−	8260.00i		−	0.403764i
$749$	1096.50	+	2122.63i	0.0534916	+	0.103550i
$750$		0			0
$751$	−5794.50	+	10036.4i	−0.281550	+	0.487660i	−0.971767	−	0.235943i	$-0.924182\pi$
$751$	−5794.50	+	10036.4i	−0.281550	+	0.487660i	0.690216	+	0.723603i	$0.257515\pi$
$752$	−2369.45	+	1368.00i	−0.114900	+	0.0663375i
$753$	−4053.00	+	2340.00i	−0.196148	+	0.113246i
$754$	−6996.00	+	12117.4i	−0.337904	+	0.585266i
$755$		0			0
$756$	3922.00	+	183.597i	0.188680	+	0.00883250i
$757$			14562.0i			0.699161i	0.936906	+	0.349581i	$0.113676\pi$
$757$			14562.0i			0.699161i	−0.936906	+	0.349581i	$0.886324\pi$
$758$	6041.39	+	3488.00i	0.289490	+	0.167137i
$759$	122.500	+	212.176i	0.00585832	+	0.0101469i
$760$		0			0
$761$	11382.5	−	19715.1i	0.542201	−	0.939120i	−0.456576	−	0.889684i	$-0.650924\pi$
$761$	11382.5	−	19715.1i	0.542201	−	0.939120i	0.998777	−	0.0494360i	$-0.0157424\pi$
$762$			1872.00i			0.0889966i
$763$	−835.715	+	17852.5i	−0.0396526	+	0.847056i
$764$	5100.00			0.241507
$765$		0			0
$766$	8717.00	+	15098.3i	0.411172	+	0.712171i
$767$	−971.681	+	561.000i	−0.0457436	+	0.0264101i
$768$	−221.703	−	128.000i	−0.0104167	−	0.00601407i
$769$	−3766.00			−0.176600			−0.0883000	−	0.996094i	$-0.528143\pi$
$769$	−3766.00			−0.176600			−0.0883000	+	0.996094i	$0.528143\pi$
$770$		0			0
$771$	1749.00			0.0816974
$772$	−121.244	−	70.0000i	−0.00565240	−	0.00326341i
$773$	23262.3	−	13430.5i	1.08239	−	0.624918i	0.150849	−	0.988557i	$-0.451799\pi$
$773$	23262.3	−	13430.5i	1.08239	−	0.624918i	0.931540	+	0.363639i	$0.118466\pi$
$774$	6760.00	+	11708.7i	0.313932	+	0.543746i
$775$		0			0
$776$	2320.00			0.107324
$777$	171.473	+	110.000i	0.00791707	+	0.00507880i
$778$			326.000i			0.0150227i
$779$	−34113.0	+	59085.4i	−1.56897	+	2.71753i
$780$		0			0
$781$	13720.0	+	23763.7i	0.628605	+	1.08878i
$782$	−715.337	−	413.000i	−0.0327115	−	0.0188860i
$783$		−	5618.00i		−	0.256412i
$784$	−5464.00	−	512.687i	−0.248907	−	0.0233549i
$785$		0			0
$786$	755.000	−	1307.70i	0.0342620	−	0.0593436i
$787$	−1816.06	+	1048.50i	−0.0822559	+	0.0474905i	−0.540564	−	0.841303i	$-0.681789\pi$
$787$	−1816.06	+	1048.50i	−0.0822559	+	0.0474905i	0.458308	+	0.888793i	$0.348456\pi$
$788$	9470.85	−	5468.00i	0.428154	−	0.247195i
$789$	2236.50	−	3873.73i	0.100914	−	0.174789i
$790$		0			0
$791$	500.000	−	779.423i	0.0224753	−	0.0350355i
$792$			7280.00i			0.326621i
$793$	2915.04	+	1683.00i	0.130537	+	0.0753658i
$794$	−999.000	−	1730.32i	−0.0446514	−	0.0773384i
$795$		0			0
$796$	−4486.00	+	7769.98i	−0.199751	+	0.345979i
$797$		−	35334.0i		−	1.57038i	−0.619254	−	0.785191i	$-0.712565\pi$
$797$		−	35334.0i		−	1.57038i	0.619254	−	0.785191i	$-0.287435\pi$
$798$	−4508.53	+	2329.00i	−0.200000	+	0.103315i
$799$	10089.0			0.446712
$800$		0			0
$801$	−11349.0	−	19657.0i	−0.500621	−	0.867101i
$802$	25559.9	−	14757.0i	1.12537	−	0.649735i
$803$	8941.71	+	5162.50i	0.392959	+	0.226875i
$804$	1756.00			0.0770265
$805$		0			0
$806$	−9900.00			−0.432646
$807$	1710.40	+	987.500i	0.0746083	+	0.0430752i
$808$	−7517.10	+	4340.00i	−0.327290	+	0.188961i
$809$	21267.5	+	36836.4i	0.924259	+	1.60086i	0.792749	+	0.609549i	$0.208649\pi$
$809$	21267.5	+	36836.4i	0.924259	+	1.60086i	0.131510	+	0.991315i	$0.458017\pi$
$810$		0			0
$811$	30676.0			1.32821			0.664106	−	0.747638i	$-0.268812\pi$
$811$	30676.0			1.32821			0.664106	+	0.747638i	$0.268812\pi$
$812$	−367.195	+	7844.00i	−0.0158695	+	0.339003i
$813$		−	8439.00i		−	0.364045i
$814$	−385.000	+	666.840i	−0.0165777	+	0.0287134i
$815$		0			0
$816$	472.000	+	817.528i	0.0202491	+	0.0350726i
$817$	−30847.8	−	17810.0i	−1.32097	−	0.762660i
$818$		−	266.000i		−	0.0113698i
$819$	−14586.0	−	28235.9i	−0.622315	−	1.20469i
$820$		0			0
$821$	−18671.5	+	32340.0i	−0.793715	+	1.37475i	0.129937	+	0.991522i	$0.458522\pi$
$821$	−18671.5	+	32340.0i	−0.793715	+	1.37475i	−0.923652	+	0.383232i	$0.874811\pi$
$822$	−4082.44	+	2357.00i	−0.173226	+	0.100012i
$823$	−2437.86	+	1407.50i	−0.103255	+	0.0596141i	−0.550738	−	0.834678i	$-0.685654\pi$
$823$	−2437.86	+	1407.50i	−0.103255	+	0.0596141i	0.447483	+	0.894292i	$0.352320\pi$
$824$	−6212.00	+	10759.5i	−0.262628	+	0.454885i
$825$		0			0
$826$	−340.000	+	530.008i	−0.0143222	+	0.0223261i
$827$		−	9276.00i		−	0.390034i	−0.980800	−	0.195017i	$-0.937524\pi$
$827$		−	9276.00i		−	0.390034i	0.980800	−	0.195017i	$-0.0624762\pi$
$828$	630.466	+	364.000i	0.0264616	+	0.0152776i
$829$	9285.50	+	16083.0i	0.389021	+	0.673805i	0.992318	−	0.123712i	$-0.0394799\pi$
$829$	9285.50	+	16083.0i	0.389021	+	0.673805i	−0.603297	+	0.797517i	$0.706147\pi$
$830$		0			0
$831$	263.500	−	456.395i	0.0109997	−	0.0190520i
$832$			4224.00i			0.176011i
$833$	16503.8	+	11711.5i	0.686464	+	0.487130i
$834$	−56.0000			−0.00232509
$835$		0			0
$836$	−9590.00	−	16610.4i	−0.396743	−	0.687179i
$837$	3442.45	−	1987.50i	0.142161	−	0.0820765i
$838$	11119.8	+	6420.00i	0.458384	+	0.264648i
$839$	−29048.0			−1.19529			−0.597645	−	0.801761i	$-0.703897\pi$
$839$	−29048.0			−1.19529			−0.597645	+	0.801761i	$0.703897\pi$
$840$		0			0
$841$	−13153.0			−0.539301
$842$	17781.2	+	10266.0i	0.727769	+	0.420178i
$843$	−174.937	+	101.000i	−0.00714728	+	0.00412648i
$844$	2344.00	+	4059.93i	0.0955969	+	0.165579i
$845$		0			0
$846$	−8892.00			−0.361363
$847$	−1744.18	+	901.000i	−0.0707563	+	0.0365510i
$848$			6672.00i			0.270186i
$849$	3974.50	−	6884.04i	0.160665	−	0.278280i
$850$		0			0
$851$	38.5000	+	66.6840i	0.00155084	+	0.00268613i
$852$	−2715.86	−	1568.00i	−0.109206	−	0.0630502i
$853$		−	32090.0i		−	1.28809i	−0.764988	−	0.644045i	$-0.777255\pi$
$853$		−	32090.0i		−	1.28809i	0.764988	−	0.644045i	$-0.222745\pi$
$854$	1887.00	+	88.3346i	0.0756110	+	0.00353952i
$855$		0			0
$856$	516.000	−	893.738i	0.0206034	−	0.0356861i
$857$	−21249.7	+	12268.5i	−0.846995	+	0.489013i	−0.859636	−	0.510907i	$-0.829310\pi$
$857$	−21249.7	+	12268.5i	−0.846995	+	0.489013i	0.0126408	+	0.999920i	$0.495976\pi$
$858$	−4001.04	+	2310.00i	−0.159199	+	0.0919139i
$859$	10412.5	−	18035.0i	0.413585	−	0.716351i	−0.581693	−	0.813408i	$-0.697610\pi$
$859$	10412.5	−	18035.0i	0.413585	−	0.716351i	0.995279	+	0.0970571i	$0.0309430\pi$
$860$		0			0
$861$	9213.00	+	431.281i	0.364667	+	0.0170709i
$862$			30426.0i			1.20222i
$863$	−19786.1	−	11423.5i	−0.780447	−	0.450591i	0.0561414	−	0.998423i	$-0.482120\pi$
$863$	−19786.1	−	11423.5i	−0.780447	−	0.450591i	−0.836589	+	0.547831i	$0.815454\pi$
$864$	−848.000	−	1468.78i	−0.0333907	−	0.0578344i
$865$		0			0
$866$	−1378.00	+	2386.77i	−0.0540720	+	0.0936554i
$867$			1432.00i			0.0560937i
$868$	−4936.34	+	2550.00i	−0.193030	+	0.0997150i
$869$	17325.0			0.676307
$870$		0			0
$871$	−14487.0	−	25092.2i	−0.563574	−	0.976139i
$872$	6685.72	−	3860.00i	0.259641	−	0.149904i
$873$	6529.83	+	3770.00i	0.253152	+	0.146157i
$874$	−1918.00			−0.0742303
$875$		0			0
$876$	−1180.00			−0.0455120
$877$	37011.3	+	21368.5i	1.42507	+	0.822763i	0.996726	−	0.0808543i	$-0.0257649\pi$
$877$	37011.3	+	21368.5i	1.42507	+	0.822763i	0.428341	+	0.903617i	$0.359098\pi$
$878$	−4785.66	+	2763.00i	−0.183950	+	0.106204i
$879$	−159.000	−	275.396i	−0.00610118	−	0.0105676i
$880$		0			0
$881$	6162.00			0.235645			0.117822	−	0.993035i	$-0.462409\pi$
$881$	6162.00			0.235645			0.117822	+	0.993035i	$0.462409\pi$
$882$	−14545.8	−	10322.0i	−0.555308	−	0.394059i
$883$		−	7748.00i		−	0.295290i	−0.989040	−	0.147645i	$-0.952831\pi$
$883$		−	7748.00i		−	0.295290i	0.989040	−	0.147645i	$-0.0471693\pi$
$884$	7788.00	−	13489.2i	0.296311	−	0.513225i
$885$		0			0
$886$	5849.00	+	10130.8i	0.221784	+	0.384142i
$887$	22450.0	+	12961.5i	0.849827	+	0.490648i	0.860592	−	0.509294i	$-0.170094\pi$
$887$	22450.0	+	12961.5i	0.849827	+	0.490648i	−0.0107656	+	0.999942i	$0.503427\pi$
$888$		−	88.0000i		−	0.00332555i
$889$	9360.00	−	14590.8i	0.353121	−	0.550461i
$890$		0			0
$891$	−11357.5	+	19671.8i	−0.427038	+	0.739651i
$892$	7011.34	−	4048.00i	0.263181	−	0.151947i
$893$	20288.4	−	11713.5i	0.760274	−	0.438944i
$894$	2295.00	−	3975.06i	0.0858571	−	0.148709i
$895$		0			0
$896$	1088.00	+	2106.17i	0.0405664	+	0.0785294i
$897$			462.000i			0.0171970i
$898$	−7936.26	−	4582.00i	−0.294918	−	0.170271i
$899$	3975.00	+	6884.90i	0.147468	+	0.255422i
$900$		0			0
$901$	12301.5	−	21306.8i	0.454853	−	0.787828i
$902$			34860.0i			1.28682i
$903$	−225.167	+	4810.00i	−0.00829798	+	0.177261i
$904$	−400.000			−0.0147166
$905$		0			0
$906$	1109.00	+	1920.84i	0.0406667	+	0.0704368i
$907$	27656.5	−	15967.5i	1.01248	−	0.584556i	0.100563	−	0.994931i	$-0.467935\pi$
$907$	27656.5	−	15967.5i	1.01248	−	0.584556i	0.911917	+	0.410375i	$0.134602\pi$
$908$	8906.21	+	5142.00i	0.325510	+	0.187933i
$909$	−28210.0			−1.02934
$910$		0			0
$911$	3408.00			0.123943			0.0619715	−	0.998078i	$-0.480261\pi$
$911$	3408.00			0.123943			0.0619715	+	0.998078i	$0.480261\pi$
$912$	1898.33	+	1096.00i	0.0689253	+	0.0397941i
$913$	−28249.7	+	16310.0i	−1.02402	+	0.591218i
$914$	−11551.0	−	20006.9i	−0.418023	−	0.724037i
$915$		0			0
$916$	3580.00			0.129134
$917$	−12423.1	+	6417.50i	−0.447381	+	0.231106i
$918$			6254.00i			0.224850i
$919$	6954.50	−	12045.5i	0.249628	−	0.432368i	−0.713795	−	0.700355i	$-0.753025\pi$
$919$	6954.50	−	12045.5i	0.249628	−	0.432368i	0.963423	+	0.267987i	$0.0863585\pi$
$920$		0			0
$921$	−4066.00	−	7042.52i	−0.145472	−	0.251964i
$922$	−16444.1	−	9494.00i	−0.587372	−	0.339120i
$923$			51744.0i			1.84526i
$924$	−1400.00	+	2182.38i	−0.0498448	+	0.0777004i
$925$		0			0
$926$	−10160.0	+	17597.6i	−0.360560	+	0.624508i
$927$	−34968.4	+	20189.0i	−1.23896	+	0.715311i
$928$	2937.56	−	1696.00i	0.103912	−	0.0599935i
$929$	−12268.5	+	21249.7i	−0.433279	+	0.750462i	−0.997153	−	0.0753990i	$-0.975977\pi$
$929$	−12268.5	+	21249.7i	−0.433279	+	0.750462i	0.563874	+	0.825861i	$0.309310\pi$
$930$		0			0
$931$	46785.5	+	4389.88i	1.64697	+	0.154536i
$932$			7148.00i			0.251224i
$933$	804.538	+	464.500i	0.0282308	+	0.0162991i
$934$	1307.00	+	2263.79i	0.0457884	+	0.0793078i
$935$		0			0
$936$	−6864.00	+	11888.8i	−0.239697	+	0.415168i
$937$		−	32758.0i		−	1.14211i	−0.820912	−	0.571055i	$-0.806534\pi$
$937$		−	32758.0i		−	1.14211i	0.820912	−	0.571055i	$-0.193466\pi$
$938$	−13686.7	−	8780.00i	−0.476424	−	0.305626i
$939$	−209.000			−0.00726353
$940$		0			0
$941$	19280.5	+	33394.8i	0.667934	+	1.15690i	0.978481	+	0.206338i	$0.0661547\pi$
$941$	19280.5	+	33394.8i	0.667934	+	1.15690i	−0.310546	+	0.950558i	$0.600512\pi$
$942$	2700.27	−	1559.00i	0.0933965	−	0.0539225i
$943$	3018.96	+	1743.00i	0.104253	+	0.0601908i
$944$	272.000			0.00937801
$945$		0			0
$946$	−18200.0			−0.625511
$947$	−34347.4	−	19830.5i	−1.17861	−	0.680470i	−0.222916	−	0.974838i	$-0.571557\pi$
$947$	−34347.4	−	19830.5i	−1.17861	−	0.680470i	−0.955692	+	0.294368i	$0.904891\pi$
$948$	−1714.73	+	990.000i	−0.0587467	+	0.0339174i
$949$	9735.00	+	16861.5i	0.332994	+	0.576763i
$950$		0			0
$951$	−7131.00			−0.243153
$952$	408.764	−	8732.00i	0.0139161	−	0.297275i
$953$			46618.0i			1.58458i	0.610144	+	0.792290i	$0.291111\pi$
$953$			46618.0i			1.58458i	−0.610144	+	0.792290i	$0.708889\pi$
$954$	−10842.0	+	18778.9i	−0.367948	+	0.637305i
$955$		0			0
$956$	10200.0	+	17666.9i	0.345075	+	0.597687i
$957$	3212.95	+	1855.00i	0.108527	+	0.0626579i
$958$			36574.0i			1.23346i
$959$	43604.5	+	2041.22i	1.46826	+	0.0687325i
$960$		0			0
$961$	12083.0	−	20928.4i	0.405592	−	0.702506i
$962$	−1257.47	+	726.000i	−0.0421439	+	0.0243318i
$963$	2904.65	−	1677.00i	0.0971973	−	0.0561169i
$964$	−8354.00	+	14469.6i	−0.279112	+	0.483437i
$965$		0			0
$966$	119.000	+	230.363i	0.00396352	+	0.00767267i
$967$			14816.0i			0.492710i	0.969180	+	0.246355i	$0.0792329\pi$
$967$			14816.0i			0.492710i	−0.969180	+	0.246355i	$0.920767\pi$
$968$	734.390	+	424.000i	0.0243845	+	0.0140784i
$969$	−4041.50	−	7000.08i	−0.133985	−	0.232069i
$970$		0			0
$971$	8437.50	−	14614.2i	0.278859	−	0.482998i	−0.692242	−	0.721665i	$-0.743377\pi$
$971$	8437.50	−	14614.2i	0.278859	−	0.482998i	0.971102	+	0.238667i	$0.0767104\pi$
$972$		−	8320.00i		−	0.274552i
$973$	436.477	+	280.000i	0.0143811	+	0.00922548i
$974$	−29906.0			−0.983830
$975$		0			0
$976$	−408.000	−	706.677i	−0.0133809	−	0.0231764i
$977$	−13715.2	+	7918.50i	−0.449119	+	0.259299i	−0.707458	−	0.706755i	$-0.750158\pi$
$977$	−13715.2	+	7918.50i	−0.449119	+	0.259299i	0.258339	+	0.966054i	$0.416825\pi$
$978$	−3898.85	−	2251.00i	−0.127476	−	0.0735982i
$979$	30555.0			0.997489
$980$		0			0
$981$	25090.0			0.816577
$982$	24858.4	+	14352.0i	0.807804	+	0.466386i
$983$	−8586.64	+	4957.50i	−0.278608	+	0.160854i	−0.632793	−	0.774321i	$-0.718092\pi$
$983$	−8586.64	+	4957.50i	−0.278608	+	0.160854i	0.354185	+	0.935175i	$0.384758\pi$
$984$	−1992.00	−	3450.25i	−0.0645352	−	0.111778i
$985$		0			0
$986$	−12508.0			−0.403992
$987$	−2665.63	−	1710.00i	−0.0859654	−	0.0551468i
$988$		−	36168.0i		−	1.16463i
$989$	−910.000	+	1576.17i	−0.0292582	+	0.0506766i
$990$		0			0
$991$	21840.5	+	37828.9i	0.700087	+	1.21259i	0.968435	+	0.249265i	$0.0801889\pi$
$991$	21840.5	+	37828.9i	0.700087	+	1.21259i	−0.268348	+	0.963322i	$0.586478\pi$
$992$	2078.46	+	1200.00i	0.0665234	+	0.0384073i
$993$		−	6571.00i		−	0.209994i
$994$	13328.0	+	25800.6i	0.425290	+	0.823286i
$995$		0			0
$996$	1864.00	−	3228.54i	0.0593003	−	0.102711i
$997$	−40801.1	+	23556.5i	−1.29607	+	0.748287i	−0.979723	−	0.200357i	$-0.935790\pi$
$997$	−40801.1	+	23556.5i	−1.29607	+	0.748287i	−0.316348	+	0.948643i	$0.602457\pi$
$998$	−9579.97	+	5531.00i	−0.303856	+	0.175432i
$999$	291.500	−	504.893i	0.00923188	−	0.0159901i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.4.j.d.149.2		4
5.2	odd	4		350.4.e.b.51.1		2
5.3	odd	4		14.4.c.b.9.1	✓	2
5.4	even	2	inner	350.4.j.d.149.1		4
7.4	even	3	inner	350.4.j.d.249.1		4
15.8	even	4		126.4.g.c.37.1		2
20.3	even	4		112.4.i.b.65.1		2
35.2	odd	12		2450.4.a.bh.1.1		1
35.3	even	12		98.4.c.e.67.1		2
35.4	even	6	inner	350.4.j.d.249.2		4
35.12	even	12		2450.4.a.bf.1.1		1
35.13	even	4		98.4.c.e.79.1		2
35.18	odd	12		14.4.c.b.11.1	yes	2
35.23	odd	12		98.4.a.b.1.1		1
35.32	odd	12		350.4.e.b.151.1		2
35.33	even	12		98.4.a.c.1.1		1
40.3	even	4		448.4.i.d.65.1		2
40.13	odd	4		448.4.i.c.65.1		2
105.23	even	12		882.4.a.k.1.1		1
105.38	odd	12		882.4.g.d.361.1		2
105.53	even	12		126.4.g.c.109.1		2
105.68	odd	12		882.4.a.p.1.1		1
105.83	odd	4		882.4.g.d.667.1		2
140.23	even	12		784.4.a.l.1.1		1
140.103	odd	12		784.4.a.j.1.1		1
140.123	even	12		112.4.i.b.81.1		2
280.53	odd	12		448.4.i.c.193.1		2
280.123	even	12		448.4.i.d.193.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.4.c.b.9.1	✓	2	5.3	odd	4
14.4.c.b.11.1	yes	2	35.18	odd	12
98.4.a.b.1.1		1	35.23	odd	12
98.4.a.c.1.1		1	35.33	even	12
98.4.c.e.67.1		2	35.3	even	12
98.4.c.e.79.1		2	35.13	even	4
112.4.i.b.65.1		2	20.3	even	4
112.4.i.b.81.1		2	140.123	even	12
126.4.g.c.37.1		2	15.8	even	4
126.4.g.c.109.1		2	105.53	even	12
350.4.e.b.51.1		2	5.2	odd	4
350.4.e.b.151.1		2	35.32	odd	12
350.4.j.d.149.1		4	5.4	even	2	inner
350.4.j.d.149.2		4	1.1	even	1	trivial
350.4.j.d.249.1		4	7.4	even	3	inner
350.4.j.d.249.2		4	35.4	even	6	inner
448.4.i.c.65.1		2	40.13	odd	4
448.4.i.c.193.1		2	280.53	odd	12
448.4.i.d.65.1		2	40.3	even	4
448.4.i.d.193.1		2	280.123	even	12
784.4.a.j.1.1		1	140.103	odd	12
784.4.a.l.1.1		1	140.23	even	12
882.4.a.k.1.1		1	105.23	even	12
882.4.a.p.1.1		1	105.68	odd	12
882.4.g.d.361.1		2	105.38	odd	12
882.4.g.d.667.1		2	105.83	odd	4
2450.4.a.bf.1.1		1	35.12	even	12
2450.4.a.bh.1.1		1	35.2	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	350.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.73205 + 1.00000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(2.00000 + 3.46410i) q^{4} +2.00000 q^{6} +(-15.5885 - 10.0000i) q^{7} +8.00000i q^{8} +(-13.0000 + 22.5167i) q^{9} +(-17.5000 - 30.3109i) q^{11} +(3.46410 + 2.00000i) q^{12} -66.0000i q^{13} +(-17.0000 - 32.9090i) q^{14} +(-8.00000 + 13.8564i) q^{16} +(51.0955 - 29.5000i) q^{17} +(-45.0333 + 26.0000i) q^{18} +(68.5000 - 118.645i) q^{19} +(-18.5000 - 0.866025i) q^{21} -70.0000i q^{22} +(-6.06218 - 3.50000i) q^{23} +(4.00000 + 6.92820i) q^{24} +(66.0000 - 114.315i) q^{26} +53.0000i q^{27} +(3.46410 - 74.0000i) q^{28} -106.000 q^{29} +(-37.5000 - 64.9519i) q^{31} +(-27.7128 + 16.0000i) q^{32} +(-30.3109 - 17.5000i) q^{33} +118.000 q^{34} -104.000 q^{36} +(-9.52628 - 5.50000i) q^{37} +(237.291 - 137.000i) q^{38} +(-33.0000 - 57.1577i) q^{39} -498.000 q^{41} +(-31.1769 - 20.0000i) q^{42} -260.000i q^{43} +(70.0000 - 121.244i) q^{44} +(-7.00000 - 12.1244i) q^{46} +(148.090 + 85.5000i) q^{47} +16.0000i q^{48} +(143.000 + 311.769i) q^{49} +(29.5000 - 51.0955i) q^{51} +(228.631 - 132.000i) q^{52} +(361.133 - 208.500i) q^{53} +(-53.0000 + 91.7987i) q^{54} +(80.0000 - 124.708i) q^{56} -137.000i q^{57} +(-183.597 - 106.000i) q^{58} +(-8.50000 - 14.7224i) q^{59} +(-25.5000 + 44.1673i) q^{61} -150.000i q^{62} +(427.817 - 221.000i) q^{63} -64.0000 q^{64} +(-35.0000 - 60.6218i) q^{66} +(380.185 - 219.500i) q^{67} +(204.382 + 118.000i) q^{68} -7.00000 q^{69} -784.000 q^{71} +(-180.133 - 104.000i) q^{72} +(-255.477 + 147.500i) q^{73} +(-11.0000 - 19.0526i) q^{74} +548.000 q^{76} +(-30.3109 + 647.500i) q^{77} -132.000i q^{78} +(-247.500 + 428.683i) q^{79} +(-324.500 - 562.050i) q^{81} +(-862.561 - 498.000i) q^{82} -932.000i q^{83} +(-34.0000 - 65.8179i) q^{84} +(260.000 - 450.333i) q^{86} +(-91.7987 + 53.0000i) q^{87} +(242.487 - 140.000i) q^{88} +(-436.500 + 756.040i) q^{89} +(-660.000 + 1028.84i) q^{91} -28.0000i q^{92} +(-64.9519 - 37.5000i) q^{93} +(171.000 + 296.181i) q^{94} +(-16.0000 + 27.7128i) q^{96} -290.000i q^{97} +(-64.0859 + 683.000i) q^{98} +910.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{4} + 8 q^{6} - 52 q^{9} - 70 q^{11} - 68 q^{14} - 32 q^{16} + 274 q^{19} - 74 q^{21} + 16 q^{24} + 264 q^{26} - 424 q^{29} - 150 q^{31} + 472 q^{34} - 416 q^{36} - 132 q^{39} - 1992 q^{41} + 280 q^{44}+ \cdots + 3640 q^{99}+O(q^{100}) \) 4 * q + 8 * q^4 + 8 * q^6 - 52 * q^9 - 70 * q^11 - 68 * q^14 - 32 * q^16 + 274 * q^19 - 74 * q^21 + 16 * q^24 + 264 * q^26 - 424 * q^29 - 150 * q^31 + 472 * q^34 - 416 * q^36 - 132 * q^39 - 1992 * q^41 + 280 * q^44 - 28 * q^46 + 572 * q^49 + 118 * q^51 - 212 * q^54 + 320 * q^56 - 34 * q^59 - 102 * q^61 - 256 * q^64 - 140 * q^66 - 28 * q^69 - 3136 * q^71 - 44 * q^74 + 2192 * q^76 - 990 * q^79 - 1298 * q^81 - 136 * q^84 + 1040 * q^86 - 1746 * q^89 - 2640 * q^91 + 684 * q^94 - 64 * q^96 + 3640 * q^99

Introduction

L-functions

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